On rational Drinfeld associators

Details On rational Drinfeld associators On rational Drinfeld associators

2010-02-11

arxiv.org/abs/1002.2331v3

Mathematics

Quantum Algebra

16 pages; v2: new section on Kontsevich knot invariant; v3: new Theorem 3.1 on construction of associators out of elements of

Scientific paper

We prove an estimate on denominators of rational Drinfeld associators. To obtain this result, we prove the corresponding estimate for the p-adic associators stable under the action of suitable elements of Gal(\bar{Q}/Q). As an application, we settle in the positive Duflo's question on the Kashiwara--Vergne factorizations of the Jacobson element J_p(x,y)=(x+y)^p-x^p-y^p in the free Lie algebra over a field of characteristic p. Another application is a new estimate on denominators of the Kontsevich knot invariant.

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